Continuous numerical solutions of coupled mixed partial di erential systems using Fer ’ s factorization

In this paper continuous numerical solutions expressed in terms of matrix exponentials are constructed to approximate time-dependent systems of the type ut −A(t)ux x −B(t)u= 0; 0¡x¡p; t ¿ 0, u(0; t)= u(p; t)= 0; u(x; 0)= f(x); 06 x6p. After truncation of an exact series solution, the numerical solution is constructed using Fer’s factorization. Given ¿ 0 and t0; t1; with 0¡t0¡t1 and D(t0; t1)= {(x; t); 06x6p; t06t6t1} the error of the approximated solution with respect to the exact series solution is less than uniformly in D(t0; t1). An algorithm is also included. c © 1999 Elsevier Science B.V. All rights reserved. AMS classi cation: 65M15, 34A50, 35C10, 35A50